What is the Greatest Common Factor of 120 and 210?

Greatest common factor (GCF) of 120 and 210 is 30.

GCF(120,210) = 30

We will now calculate the prime factors of 120 and 210, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 120 and 210.

How to find the GCF of 120 and 210?

We will first find the prime factorization of 120 and 210. After we will calculate the factors of 120 and 210 and find the biggest common factor number .

Step-1: Prime Factorization of 120

Prime factors of 120 are 2, 3, 5. Prime factorization of 120 in exponential form is:

120 = 2³ × 3¹ × 5¹

Step-2: Prime Factorization of 210

Prime factors of 210 are 2, 3, 5, 7. Prime factorization of 210 in exponential form is:

210 = 2¹ × 3¹ × 5¹ × 7¹

Step-3: Factors of 120

List of positive integer factors of 120 that divides 120 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60

Step-4: Factors of 210

List of positive integer factors of 210 that divides 120 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 120 and 210. The biggest common factor number is the GCF number.
So the greatest common factor 120 and 210 is 30.

Also check out the Least Common Multiple of 120 and 210